Question

# Calculate the speed of a galaxy emitting light of wavelength$5.48 \times 10 ^ { - 7 } \mathrm { m }$which when received on Earth is measured to have a wavelength of$5.65 \times 10 ^ { - 7 } \mathrm { m }$.

Solution

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We can use the following relation to find the speed of the galaxy

$\frac{\Delta \lambda}{\lambda}=\frac{v}{c}$

where $(v)$ is the speed of the galaxy and $(c)$ is the speed of light in space. Let's rearrange the relation to isolate $(v)$

$v=c\times \frac{\Delta \lambda}{\lambda}=(3\times 10^{8} \mathrm{~ m/s}) \times \frac{5.65\times 10^{-7} \mathrm{~ m}-5.48\times 10^{-7} \mathrm{~ m}}{5.48\times 10^{-7} \mathrm{~ m}}$

$v=9.3 \times 10^{6} \mathrm{~ m/s}$

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